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The influence of the degree of asymmetry of a Permalloy ring on the switching behavior and vortex configuration was studied by changing the diameter of the circle and its shift length. The object oriented micromagnetic framework software was used to simulate the magnetic configurations and reversal processes in a single asymmetric Permalloy ring. By introducing an inner circle shifted from the center of the outer circle by a shift length, an asymmetric ring and asymmetric ratio are defined. The vortex nucleation (Hn) and vortex annihilation (Han) fields, analyzed from the simulated hysteresis loops with 300, 500, and 800 nm outer diameters, have linear relations to the asymmetric ratio. It is noteworthy that a linear relationship for Hn is independent on the variation of the inner diameters and is only dependent on the asymmetric ratio. This result demonstrates that an asymmetric ring could determine not only the vortex chirality, but also the vortex nucleation and annihilation fields.